Question: Solve for $x$ and $y$ using elimination. ${4x-2y = 0}$ ${-5x+2y = -2}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $-x = -2$ $\dfrac{-x}{{-1}} = \dfrac{-2}{{-1}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {4x-2y = 0}\thinspace$ to find $y$ ${4}{(2)}{ - 2y = 0}$ $8-2y = 0$ $8{-8} - 2y = 0{-8}$ $-2y = -8$ $\dfrac{-2y}{{-2}} = \dfrac{-8}{{-2}}$ ${y = 4}$ You can also plug ${x = 2}$ into $\thinspace {-5x+2y = -2}\thinspace$ and get the same answer for $y$ : ${-5}{(2)}{ + 2y = -2}$ ${y = 4}$